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Permutations and Combinations · Discussion forum

Hard Level Question 8 – answer, explanation & discussion

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Question 8 Back to Exercise

How many solutions in non-negative integers does x + y + z + w = 20 have if x ≥ 2?

  • A 1,771
  • B 1,540
  • C 1,330 Correct
  • D 969
Correct Answer: Option C

Let x = 2 + x′: x′ + y + z + w = 18

(18 + 3)C3 = 21C3 = 1,330

Trap: 1,771 = 23C3 ignores x ≥ 2.

Answer: 1,330

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